Question

Consider the following expression and the simplified expression. Expression Simplified Expression 3 x squared + 5 y squared box + 3 box + 4 y squared + 6 9 x squared minus y squared + 9 Which terms could be in the boxes to make the expressions equivalent? Positive 6 x squared and Negative 6 y squared Positive 6 x squared and Negative 10 y squared Positive 9 x squared and Negative 10 y squared Positive 9 x squared and Negative 6 y squared

Answer 1

The correct answer is B. Positive 6 x squared and Negative 10 y squared

Explanation:

Answer 2

The correct answer is:

`+6x^(2)\\-9y^2`

Explanation:

We are given the term:

`3x^(2) +5y^(2) [\text{ \ }] +3 [\text{ \ }] +4y^(2) +6 = 9x^(2) -y^(2) +9`

We have to fill in to the empty spaces such that the above equation gets satisfied.

First of all, let us simplify the LHS (Left Hand Side):

`3x^(2) +5y^(2) [\text{ \ }] +3 [\text{ \ }] +4y^(2) +6\\\Rightarrow 3x^(2) +5y^(2) +4y^(2) [\text{ \ }] [\text{ \ }] +6 +3\\\Rightarrow 3x^(2) +9y^(2) [\text{ \ }] [\text{ \ }] +9`

Now, let us equate the LHS and RHS (Right Hand Side):

`\Rightarrow 3x^(2) +9y^(2) [\text{ \ }] [\text{ \ }] +9 = 9x^(2) -y^(2) +9`

Equating the coefficients of
`x^(2)\ and\ y^(2)` in LHS and RHS:

One box will have value =
`9x^(2) -3x^(2) =+6x^(2)`

Other box will have value =
`-y^(2) -9y^(2) =-10y^(2)`

The correct answer is:

`+6x^(2)\\-9y^2`

So, if we fill the boxes with above values, the expression will be simplified as given.